Beam homogenizer, laser illumination apparatus and method, and semiconductor device

ABSTRACT

A beam homogenizer at least includes a first optical lens for dividing a light beam into N(n&#39;-1) beams in a vertical direction, a second optical lens for dividing the light beam into (2n+1) beams in a horizontal direction, a third optical lens for recombining the beams that are divided in the vertical and horizontal directions into (n&#39;-1) beams while superimposing the (n&#39;-1) beams so that they are deviated from each other in the horizontal direction, and a fourth optical lens for recombining the beams that are divided in the vertical direction.

This is a divisional of U.S. application Ser. No. 09/438,019, filed Nov.10, 1999, now U.S. Pat. No. 6,301,727 which is a divisional ofapplication Ser. No. 09/163,296, filed Sep. 29, 1998, 6,002,523.

FIELD OF THE INVENTION

The present invention relates to a technique capable of applying a laserbeam to a large area with a high degree of uniformity as well as anapplication method of that technique.

BACKGROUND OF THE INVENTION

In recent years, extensive studies have been made of techniques ofcrystallizing an amorphous semiconductor film or improving thecrystallinity of a crystalline semiconductor film (i.e., anon-single-crystal semiconductor film that is polycrystalline,microcrystalline or of like crystallinity) formed on an insulatingsubstrate such as a glass substrate by subjecting it to laser annealing.A typical example of such a semiconductor film is a silicon film.

Glass substrates are advantageous over quartz substrates that havewidely been used conventionally in that they are inexpensive and high inworkability and can easily provide a large-area substrate. This is thereason why the above studied have been made. The reason why lasers areused favorably in crystallization is that glass substrates have lowmelting points. Lasers can apply high energy to only anon-single-crystal film without changing the temperature of a substrateto a large extent.

Having high mobility, crystalline silicon films that are formed by laserannealing are widely used in monolithic liquid crystal electro-opticaldevices and the like in which pixel-driving TFTs (thin-film transistors)and driver circuit TFTs, for instance, are formed on a single glasssubstrate by using such a crystalline silicon film. Since a crystallinesilicon film formed by laser annealing is constituted of a number ofcrystal grains, it is called a polysilicon film or a polycrystallinesemiconductor film.

A laser annealing method in which a pulse laser beam emitted from alarge output power excimer laser or the like is processed by an opticalsystem so as to be shaped into a several centimeters square spot or alinear beam of several millimeters in width and tens of centimeters inlength and scanning is made with the processed laser beam (i.e., a laserbeam illumination position is moved relative to an illumination surface)is favorably used because it provides high mass-productivity and issuperior from the industrial point of view.

In particular, in contrast to the case of using a spot-like laser beamthat requires scanning in two orthogonal directions, the use of a linearlaser beam can provide high mass-productivity because the entireillumination subject surface can be illuminated with laser light byscanning it with the linear laser beam only in the directionperpendicular to its length direction. The scanning is made in thedirection perpendicular to the length direction because the scanning insuch a direction is most efficient. Because of the highmass-productivity, the use of a linear laser beam is now becoming themainstream in the laser annealing.

There are several problems in the case of performing laser annealing ona non-single crystal semiconductor film by scanning it with a pulselaser beam that has been processed into a linear shape. Among thoseproblems, one of the particularly serious problems is that laserannealing is not performed uniformly over the entire film surface. Whenlinear laser beams started to be used, there occurred a markedphenomenon that stripes were formed at beam overlapping portions. A filmshowed much different electrical characteristics from one stripe toanother.

FIG. 1A shows how such stripes are formed. Stripes appear depending onthe manner of light reflection when the surface of a laser-annealedsilicon film is observed.

FIG. 1A is of a case where a linear laser beam extending in theright-left direction in the paper surface that is emitted from a XeClexcimer laser is applied while scanning is made in the top-to-bottomdirection in the paper surface. It is understood that the stripes ofFIG. 1A originate from the manner of overlapping of shots of pulse laserbeams.

Where an active matrix liquid crystal display was manufactured by usinga silicon film that exhibits stripes as shown in FIG. 1A, there occurreda problem that similar stripes appeared on the screen. This problem isnow being solved by improving a non-single crystal semiconductor film asa subject of laser beam illumination and making the linear laser beamscanning pitch (interval between adjacent linear laser beams) finer.

As the above type of stripes become less conspicuous, non-uniformity inthe energy profile of a beam itself comes to appear.

In general, in forming a linear laser beam, an original rectangular beamis processed into a linear shape by inputting it to a proper opticalsystem. A rectangular beam having an aspect ratio of 2 to 5 is modifiedinto a linear beam having an aspect ratio of 100 or more by an opticalsystem of FIG. 2, for instance. This optical system is so designed thatthe intrabeam energy profile is uniformized at the same time.

The apparatus of FIG. 2 has a function of converting a laser beamemitted from an oscillator 201 (approximately rectangular at this stage)into a linear beam with an optical system denoted by reference numerals202-204, 206, and 208 and applying the linear beam. Reference numerals205 and 207 denote a slit and a mirror, respectively.

A cylindrical lens group (also called a multiple cylindrical lens) 202has a function of dividing a beam into many beams. The many dividedbeams are combined by a cylindrical lens 206.

The above components are needed to improve the intrabeam intensityprofile. A combination of a cylindrical lens group 203 and a cylindricallens 204 has the same function as the combination of the cylindricallens group 202 and the cylindrical lens 206.

That is, the combination of the cylindrical lens group 202 and thecylindrical lens 206 has a function of improving the intensity profileof a linear laser beam in the longitudinal direction and the combinationof the cylindrical lens group 203 and the cylindrical lens 204 has afunction of improving the intensity profile of a linear laser beam inthe width direction.

An optical system having a role of uniformizing the intrabeam energyprofile is called a beam homogenizer. The optical system of FIG. 2 isalso a beam homogenizer. One method of uniformizing the energy profileis to divide an original rectangular beam, enlarging the divided beams,and then combining the enlarged beams.

It appears that a beam that has been reconstructed after dividing anoriginal beam in the above manner would have a higher degree ofuniformity in energy profile as the beam division is made finer.However, when a beam obtained in the above manner was actually appliedto a semiconductor film, stripes as shown in FIG. 1B occurred in thefilm in spite of fine beam division.

Like the case of FIG. 1A, FIG. 1B is of a case where a linear laser beamextending in the right-left direction in the paper surface that wasemitted from a XeCl excimer laser was applied to a silicon film whilescanning was made in the top-to-bottom direction in the paper surface.However, in the case of FIG. 1B, the scanning conditions were setproperly so that no marked stripes as shown in FIG. 1A appear.

As shown in FIG. 1B, innumerable stripes are formed perpendicularly tothe longitudinal direction of a linear laser beam. Stripes of this typeshould be formed due to a striped energy profile of an originalrectangular beam or the optical system.

To investigate whether stripes were caused by a striped energy profileof an original rectangular beam or the optical system, the inventorsconducted a simple experiment. In the experiment, it was studied howstripes varied as a rectangular laser beam was rotated before enteringthe optical system.

No variation was observed at all. Therefore, it was confirmed that theoptical system caused stripes rather than an original rectangular beam.It is concluded that stripes are an interference fringe of light becausethe optical system uniformizes the energy profile of asingle-wavelength, phase-equalized beam (a laser beam is phase-equalizedbecause a laser produces high-intensity light by equalizing the phase)by dividing it and combining the divided beams.

FIG. 3 illustrates a light interference fringe 302 in a linear laserbeam 301 that is formed by the optical system of FIG. 2. In FIG. 3,symbol I represents the laser light intensity. The interference fringe302 is produced in such a manner that when beams obtained by dividing anoriginal beam by the cylindrical lens groups 202 and 203 of the opticalsystem of FIG. 2 are combined by the cylindrical lenses 204 and 206, thedivided beams interfere with each other and a stationary wave is therebyformed in the beam.

That is, the reason why sharp, periodic interference peaks are generatedis that divided beams are superimposed one on another in the same regionon an illumination surface.

As shown in FIG. 3, the amplitude of waves varies periodically. In thecase of the optical system of FIG. 2, three waves are formed per oneperiod in the longitudinal direction of a linear beam.

The number n of waves (i.e., the number of interference peaks) per pitchand the number s of lenses of the cylindrical lens group 202 satisfy thefollowing relationship:

n=(s−1)/2(s: odd number)

n=s/2(s: even number)

In the optical system of FIG. 2, the number n is equal to 3 because thenumber s of lenses of the cylindrical lens group 202 is 7 (odd number).

In this case, an interference state shown in FIG. 4A is obtained. FIG.4A, which was obtained by a computer calculation, shows an interferencestate in a linear laser beam at a certain time point. The horizontalaxis of FIG. 4A corresponds to the position in the longitudinaldirection of a linear laser beam, and the square of a value on thevertical axis of FIG. 4A corresponds to the light intensity in an actualinterference state. For example, the interference state of FIG. 4A isactually observed as the light intensity profile shown in FIG. 3.

Where the number s of lenses of the cylindrical lens group 202 is equalto 8, an interference pattern as shown in FIG. 4B is obtained.

In FIGS. 4A and 4B, the square of the amplitude represents the strengthof interference (i.e., the degree of an action that beams having thesame phase intensify each other) and parameter d is defined as the pitchof interference peaks.

The curves of FIGS. 4A and 4B were obtained by a computer simulation andactual interference fringes of laser beams do not exhibit so clearstrong and weak portions. This is considered due to dispersion,refraction, and loss of light that are caused by slight deviations inthe optical system, the materials of the components of the opticalsystem, and processing errors of the optical system, energy dispersionin a semiconductor film that is caused by heat conduction, and otherfactors.

SUMMARY OF THE INVENTION

An object of the present invention is to lower the degree ofillumination unevenness of a linear laser beam.

Each aspect of the invention will be described below. In the followingdescription, N is a natural number, n is an integer that is greater thanor equal to 3, and n′ is an integer that satisfies 3≦n′≦n.

According to a first aspect of the invention, there is provided a beamhomogenizer having a function of forming a sinusoidal stationary wave onan illumination surface by dividing a laser beam and recombining dividedlaser beams.

According to a second aspect of the invention, there is provided a beamhomogenizer comprising a first optical lens for dividing a light beaminto N(n′−1) beams in a vertical direction; a second optical lens fordividing the light beam into (2n+1) beams in a horizontal direction; athird optical lens for recombining the beams that are divided in thevertical and horizontal directions into (n′−1) beams while superimposingthe (n′−1) beams so that they are deviated from each other in thehorizontal direction; and a fourth optical lens for recombining thebeams that are divided in the vertical direction.

According to a third aspect of the invention, there is provided a beamhomogenizer comprising a first optical lens for dividing a light beaminto N(n−1) beams in a vertical direction; a second optical lens fordividing the light beam into (2n+1) beams in a horizontal direction; athird optical lens for recombining the beams that are divided in thevertical and horizontal directions into (n−1) beams while superimposingthe (n−1) beams so that they are deviated from each other in thehorizontal direction; and a fourth optical lens for recombining thebeams that are divided in the vertical direction.

According to a fourth aspect of the invention, there is provided a beamhomogenizer comprising a first optical lens for dividing a light beaminto N(n′−1) beams in a vertical direction; a second optical lens fordividing the light beam into (2n) beams in a horizontal direction; athird optical lens for recombining the beams that are divided in thevertical and horizontal directions into (n′−1) beams while superimposingthe (n′−1) beams so that they are deviated from each other in thehorizontal direction; and a fourth optical lens for recombining thebeams that are divided in the vertical direction.

According to a fifth aspect of the invention, there is provided a beamhomogenizer comprising a first optical lens for dividing a light beaminto N(n−1) beams in a vertical direction; a second optical lens fordividing the light beam into (2n) beams in a horizontal direction; athird optical lens for recombining the beams that are divided in thevertical and horizontal directions into (n−1) beams while superimposingthe (n−1) beams so that they are deviated from each other in thehorizontal direction; and a fourth optical lens for recombining thebeams that are divided in the vertical direction.

According to a sixth aspect of the invention, there is provided a laserillumination apparatus comprising means for generating a laser beam; abeam homogenizer comprising an optical lens for dividing the laser beaminto N(n′−1) beams in a vertical direction; a cylindrical lens group fordividing the laser beam into (2n+1) beams in a horizontal direction;(n′−1) cylindrical lenses for recombining the beams that are divided inthe horizontal direction while superimposing the divided beams so thatthey are deviated from each other by d/(n′−1) in the horizontaldirection; and a cylindrical lens for recombining the beams that aredivided in the vertical direction; and a moving table that is movable inone direction, wherein d is defined as an interval of peaks of aninterference fringe that is formed on an illumination surface by a beamthat has passed through one of the (n′−1) cylindrical lenses.

According to a seventh aspect of the invention, there is provided alaser illumination apparatus comprising means for generating a laserbeam; a beam homogenizer comprising an optical lens for dividing thelaser beam into N(n−1) beams in a vertical direction; a cylindrical lensgroup for dividing the laser beam into (2n+1) beams in a horizontaldirection; (n−1) cylindrical lenses for recombining the beams that aredivided in the horizontal direction while superimposing the dividedbeams so that they are deviated from each other by d/(n−1) in thehorizontal direction; and a cylindrical lens for recombining the beamsthat are divided in the vertical direction; and a moving table that ismovable in one direction, wherein d is defined as an interval of peaksof an interference fringe that is formed on an illumination surface by abeam that has passed through one of the (n−1) cylindrical lenses.

According to an eighth aspect of the invention, there is provided alaser illumination apparatus comprising means for generating a laserbeam; a beam homogenizer comprising an optical lens for dividing thelaser beam into N(n′1) beams in a vertical direction; a cylindrical lensgroup for dividing the laser beam into (2n) beams in a horizontaldirection; (n′−1) cylindrical lenses for recombining the beams that aredivided in the horizontal direction while superimposing the dividedbeams so that they are deviated from each other by d/(n′−1) in thehorizontal direction; and a cylindrical lens for recombining the beamsthat are divided in the vertical direction; and a moving table that ismovable in one direction, wherein d is defined as an interval of peaksof an interference fringe that is formed on an illumination surface by abeam that has passed through one of the (n′−1) cylindrical lenses.

According to a ninth aspect of the invention, there is provided a laserillumination apparatus comprising means for generating a laser beam; abeam homogenizer comprising an optical lens for dividing the laser beaminto N(n−1) beams in a vertical direction; a cylindrical lens group fordividing the laser beam into (2n) beams in a horizontal direction; (n−1)cylindrical lenses for recombining the beams that are divided in thehorizontal direction while superimposing the divided beams so that theyare deviated from each other by d/(n−1) in the horizontal direction; anda cylindrical lens for recombining the beams that are divided in thevertical direction; and a moving table that is movable in one direction,wherein d is defined as an interval of peaks of an interference fringethat is formed on an illumination surface by a beam that has passedthrough one of the (n−1) cylindrical lenses.

In the sixth to ninth aspects of the invention, d may be approximatelyexpressed by d=λf/L, where λ is the wavelength of the laser beam, f isthe focal length of the (n′−1) or (n−1) cylindrical lenses, and L is thewidth of each constituent lens of the cylindrical lens group.

The invention is particularly effective if on the illumination surfacethe laser beam is a linear beam having a longer axis in the horizontaldirection.

In general, the laser beam is an excimer laser beam.

It is preferable that the moving direction of the moving table bevariable.

To avoid misunderstanding, it is noted that in the specification thehorizontal and vertical directions mean the longitudinal direction andthe width direction, respectively, of a linear laser beam.

According to a 10th aspect of the invention, there is provided asemiconductor device manufactured by using a semiconductor film that hasbeen formed by laser annealing that uses a laser beam produced by thebeam homogenizer according to the first aspect of the invention.

According to an 11th aspect of the invention, there is provided asemiconductor device manufactured by using a semiconductor film that hasbeen formed by laser annealing that uses a laser beam produced by thebeam homogenizer according to the second aspect of the invention.

According to a 12th aspect of the invention, there is provided asemiconductor device manufactured by using a semiconductor film that hasbeen formed by laser annealing that uses a laser beam produced by thebeam homogenizer according to the fourth aspect of the invention.

In crystallizing or improving the crystallinity of a non-single-crystalsemiconductor film by using a laser beam that has been processed into alinear shape by dividing an original laser beam and recombining thedivided beams, the invention prevents a processed semiconductor filmfrom reflecting light-interference-induced periodic energy unevenness inthe linear laser beam.

For example, the energy profile of a linear laser beam that is formed bythe optical system of FIG. 2 has a periodic intensity pattern in thelongitudinal direction as shown in FIGS. 4A and 4B. If a linear laserbeam having such an energy profile is applied to a semiconductor film, aprocessed semiconductor film exactly reflects the energy profile.

By using a new beam homogenizer, the invention makes the interferenceprofile in a linear laser beam much more distributed (see FIGS. 7A-7G)than obtained by conventional beam homogenizers, and thereby uniformizesthe energy profile in the linear laser beam. This enables laserannealing to produce a result having a higher degree of uniformity.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are photographs of silicon films that were crystallizedby laser annealing that used a linear laser beam;

FIGS. 2A and 2B, and 2C show a conventional optical system for forming alinear laser beam and an optical path thereof;

FIGS. 3 and 4A-4B illustrate light interference in a linear laser beamthat is formed by the conventional optical system;

FIGS. 5A, 5B, 5C, and 6 show an optical system for forming a linearlaser beam according to a first embodiment of the invention and anoptical path thereof;

FIGS. 7A-7G show methods of superimposing interference fringes formaking light interference less conspicuous;

FIGS. 8A and 8B illustrate a difference in arrangement between anoptical system that produces spherical waves and an optical system thatproduces a plane waves;

FIG. 9 shows a laser illumination system according to the firstembodiment;

FIG. 10 is a top view of a laser annealing apparatus according to thefirst embodiment;

FIGS. 11A and 11B show examples of a concave/convex-mixed cylindricallens group and a multi-phase lens, respectively;

FIGS. 12 and 13 show parameters that are necessary for determining thepitch d of an interference fringe through a calculation; and

FIG. 14 shows an optical system for forming a linear laser beamaccording to the first embodiment and an optical a path thereof.

DETAILED DESCRIPTION OF THE INVENTION

In the optical system of FIG. 2, if the cylindrical lens 206 is dividedalong a broken line 210 and the divided parts are deviated from eachother by a proper distance in the direction perpendicular to the papersurface, beams that pass through the upper half of the cylindrical lens206 and beams that pass through the lower half are superimposed on eachother on the illumination surface so as to be deviated from each otherproperly, whereby a different beam interference pattern is formed. Byutilizing this phenomenon in a proper manner, that is, by properlysetting the offset of the top and bottom divisional lenses of thecylindrical lens 206, interference peaks in a beam can be distributedevenly. This is apparent from the principle of superposition of waves.

FIGS. 5 and 6 show such an optical system. A cylindrical lens 501 inFIG. 5 corresponds to the top/bottom-divided version of the cylindricallens 206 in FIG. 2. FIG. 6 is a perspective view of the optical systemof FIG. 5. The mirror 207 that is shown in FIG. 5 is omitted in FIG. 6.

The invention is intended to determine features of an optical systemthat can distribute interference peaks most efficiently.

FIG. 7A shows an interference fringe pattern that is produced by theapparatus of FIG. 2 when the number of lenses of the cylindrical lensgroup 202 is seven. The square of a value of the interference fringepattern corresponds to the light intensity. The right-left direction ofFIG. 7A corresponds to the longitudinal direction of a linear laserbeam. Parameter d is defined as the length of the one period of theinterference fringe pattern of FIG. 7A. The one period is in accordancewith the pitch of the interference fringe.

The inventors performed computer calculations to search for a patternthat was obtained by adding patterns like the pattern of FIG. 7A and inwhich interference peaks were distributed most evenly. The best patternwas obtained when two patterns of FIG. 7A were shifted from each otherby a half pitch and then superimposed on each other.

Specifically, when the pattern of FIG. 7A was superimposed on a patternof FIG. 7B that was obtained by shifting the pattern of FIG. 7A by halfperiod, a pattern of FIG. 7C was obtained.

In the pattern of FIG. 7C, the degree of interference is moredistributed than in the patterns of FIGS. 7A and 7B.

FIG. 7D shows an interference fringe pattern that is produced by theapparatus of FIG. 2 when the number of lenses of the cylindrical lensgroup 202 is nine. Parameter d is defined as the one period of theinterference fringe pattern of FIG. 7D.

The inventors performed computer calculations to search for a patternthat was obtained by adding patterns like the pattern of FIG. 7D and inwhich interference peaks were distributed most evenly. The best patternwas obtained when three patterns of FIG. 7D were shifted from each otherby ⅓ period and then superimposed one on another (see FIG. 7G).

Specifically, interference patterns of FIGS. 7E and 7F were produced byshifting the interference pattern of FIG. 7D by a ⅓ pitch and a ⅔ pitch,respectively. When the interference patterns of FIGS. 7D-7F weresuperimposed one on another, an interference pattern of FIG. 7G wasobtained.

In the interference pattern of FIG. 7G, the degree of interference ismuch more distributed than in the interference patterns of FIGS. 7D-7F.

To realize the above superposition, it is necessary to produce laserbeams having interference states of FIGS. 7A and 7B, for instance.

A laser beam produced by the combination of the cylindrical lens group202 and the cylindrical lens 206 is also divided into a plurality ofbeams by the cylindrical lens group 203. Therefore, by causing thedivided laser beams that are produced by the cylindrical lens group 203to be superimposed one on another so as to be deviated from one anotherwith subtle positional relationships, a laser beam having interferencepeaks that are more distributed than in FIGS. 7C and.7G can be obtained.

The cylindrical lens 501 plays a role of shifting laser beams. Forexample, where the number of lenses of the cylindrical lens group 202 isseven, a laser beam as shown in FIG. 7C can be obtained by using thecylindrical lens 501 that is divided into two parts, that is, top andbottom parts. In this case, it is preferable that the cylindrical lensgroup 203 divide a laser beam into an even number of beams. If this isthe case, resulting laser beams are properly distributed to the top andbottom lenses as shown in the bottom part of FIG. 5 and hence nodistortion occurs in the optical paths of the laser beams. In the caseof FIG. 5, since the cylindrical lens 203 produces four beams, two beamsenter each of the top and bottom lenses of the cylindrical lens 501.

Where the number of lenses of the cylindrical lens group 202 is nine, alaser beam as shown in FIG. 7G can be obtained by using the cylindricallens 501 that is divided into three parts, that is, top, middle, andbottom parts. In this case, it is preferable that the cylindrical lensgroup 203 divide a laser beam into a multiple-of-3 beams. If this is thecase, resulting laser beams are properly distributed to the top, middleand bottom lenses and hence no distortion occurs in the optical paths ofthe laser beams.

However, the cylindrical lens 501 is divided into three or more parts,the alignment of the optical system becomes unduly complex. Therefore,the cylindrical lens 501 may be divided into two parts rather than threeparts. Interference peaks were properly distributed even bysuperimposing two laser beams as shown in FIG. 7D that are shifted fromeach other by a half pitch. In this case, the cylindrical lens 501 is ofa type that is divided into two parts, that is, top and bottom parts.The cylindrical lens group 203 may divide a laser beam into amultiple-of-2 beams.

The invention provides an optimum combination of parameters for theabove-described scheme. That is, the invention is intended to determinefeatures of an optical system that can distribute interference peaksmost efficiently.

In the following description, N is assumed to be a natural number whilethe number n of the interference peaks per one period in thelongitudinal direction of a linear laser beam is an integer that isgreater than or equal to 3. In the optical system of FIG. 5, N=2 andn=3. This is because when n=3, the number s of lenses of the cylindricallens group 202 is seven and the number N(n=1) of lenses of thecylindrical lens group 203 is four.

In FIGS. 4A-4B and 7A-7G, parameter d indicates the interval (the lengthof one period) of an interference pattern that is formed on theillumination surface by a beam that has passed through one of the lensesthat constitute the cylindrical lens 501. The value of d can be obtainedby observing a laser beam that is produced when the cylindrical lens 501is covered except one constituent lens, or observing annealing effect orthe like of that laser beam. The value of d can also be calculated asdescribed later in the third embodiment.

A description will now be made of a proper deviation between theconstituent lenses of the cylindrical lens 501 to obtain the effect ofthe invention.

Where the number of lenses of the cylindrical lens group 202 is seven, nis equal to 3 and hence the number of lenses of the cylindrical lensgroup 203 may be a multiple of (n−1), that is, an even number. In thiscase, the top and bottom lenses of the cylindrical lens 501 may bedeviated from each other by a distance d/2.

Where the number of lenses of the cylindrical lens group 202 is nine, nis equal to 4 and hence a beam that is sufficiently uniform can beobtained if the number of lenses of the cylindrical lens group 203 is amultiple of 3 (i.e., (n=1)), for instance, 6. A beam that is higher inthe degree of uniformity can be obtained when the cylindrical lens 501is divided into three parts than two parts. In the former case, the top,middle, and bottom lenses of the cylindrical lens 501 may be deviatedfrom each other by a distance d/3.

However, because of the structure of the optical system, the alignmentof the optical system becomes more difficult when the cylindrical lens501 is divided into three or more parts. For example, the cylindricallens 501 may be divided into two parts even in a case where a beam thatis higher in the degree of uniformity can be obtained by designing theoptical system using the 3-piece-divided cylindrical lens 501.

From the above discussions and calculations, it is understood that wherethe number of lenses of the cylindrical lens group 202 is an odd number,the cylindrical lens 501 may be divided into (n′−1) parts and the (n′−1)lenses may be deviated from each other by d/(n′−1), where n′ is aninteger in a range of 3≦n′≦n. In this case, satisfactory results wereobtained when the cylindrical lens group 203 had N(n′−1) constituentlenses.

With the above design, divided laser beams produced by the cylindricallens group 203 can be superimposed one on another in a manner as shownin FIGS. 7A-7G and a laser beam having a uniformized interference stateas shown in FIG. 7C or 7G can be obtained.

The configuration of the optical system shown in FIGS. 5 and 6 is thebasic one and other optical systems may be used. Part of the lenses maybe replaced by lenses having similar functions. Further, the opticalsystem of FIGS. 5 and 6 may be used as part of the entire opticalsystem. For example, although the cylindrical lens group 202 and thecylindrical lens group 203 are convex lens groups, they may be concavelens groups or concave/convex-mixed lens groups.

A laser beam may be divided by a method other than the method usingcylindrical lenses. For example, the cylindrical lens group 203 and thecylindrical lens 204 may be replaced by multi-phase lenses having almostthe same functions (see FIG. 11B).

The above configuration is particularly effective in converting a laserbeam whose aspect ratio is not very large into a linear laser beamhaving an aspect ratio of 100 or more.

In contrast to the case where the number of lenses of the cylindricallens group 202 is an odd number, remarkable effect is not obtained whenit is an even number. (It goes without saying that the cylindrical lensgroup 202 can be regarded as being constituted of an odd number oflenses when laser beams corresponding to an odd-numbered part of thecylindrical lens group 202 are substantially used by the downstreamlenses even if the cylindrical lens group 202 is constituted of an evennumber of lenses.)

Where the number of lenses of the cylindrical lens group 202 is an oddnumber, it is possible to produce a beam having a sinusoidalinterference profile as shown in FIGS. 7C and 7G in which interferencepeaks are more distributed in the beam. Where the number of lenses ofthe cylindrical lens group 202 is 2 or 3, a beam having a sinusoidalinterference profile can be obtained by the optical system of FIG. 2.However, since the number of divided beams is insufficient, it isdifficult to obtain a uniform beam. The invention is epoch-makingbecause it enables use of a sufficient number of divided beams andprovides a beam having a sinusoidal interference profile.

Where the number of lenses of the cylindrical lens group 202 is an evennumber, a beam having so clearly distributed interference peaks cannotbe obtained. However, even in this case, marked improvement is obtainedas compared to the conventional optical system (see FIG. 2). That is,the effect of distributing the interference and thereby correctingillumination unevenness can be obtained.

Also where the number of lenses of the cylindrical lens group 202 is aneven number, the cylindrical lens 501 may be divided into (n′−1) partsand the (n′−1) lenses may be deviated from each other by d/(n′−1). Withthis design, interference peaks were distributed properly. In this case,parameter d is defined as shown in FIG. 4B. Satisfactory results wereobtained when the cylindrical lens group 203 was constituted of N(n′−1)lenses.

Incidentally, parameter d is defined as the pitch (the length of oneperiod) of interference peaks as shown in FIG. 4A or 4B, that is, thepitch of an interference state appearing in a beam (linear laser beam)that corresponds to one constituent cylindrical lens of the cylindricallens 501.

As is understood from the above description, it is preferable that theintervals d of an interference fringe be constant in a laser beam. Thatis, it is preferable that interference peaks appear at a fixed period inthe longitudinal direction of a linear beam as shown in FIGS. 4A and 4B.

However, except for certain special cases, the intervals betweeninterference peaks in a linear laser beam produced by the optical systemof FIG. 2 are not constant. This is because a linear beam is obtained bycombining spherical waves. (See FIG. 8A. When a spherical wave is cut bya straight line, intervals between points having the same phase are notconstant.)

When it is necessary to make the intervals of interference peaksapproximately constant, one method is to combine plane waves into alinear shape. (When a plane wave is cut obliquely by a straight line,intervals between points having the same phase become constant.)

FIG. 8B shows an optical system for forming such light waves. Thisoptical system is different from the optical system of FIG. 8A in thatall the divided laser beams produced by the incident-side cylindricallens are converted into parallel beams by the downstream cylindricallens.

This type of optical system can easily be obtained by properly settingthe distance between the front and rear cylindrical lenses. With thisdesign, any of the divided beams produced by the cylindrical lens groupcan be converted into a plane wave by the cylindrical lens. When a beamproduced by this optical system is used, the intervals between verticalstripes becomes approximately constant. The optical system having thisarrangement is most suitable for the invention.

However, even a linear beam obtained by combining spherical waves cansubstantially be regarded as being constituted of parallel beams becausethe radius of curvature of the spherical waves is sufficiently large.Therefore, the invention can also be utilized for such a case. In thiscase, the interval d of an interference fringe is defined as the averageof all intervals.

As described above, the degree of uniformity of an interference fringeprofile of a linear laser beam can greatly be increased by utilizing theinvention. In particular, where the cylindrical lens group 202 isconstituted of an odd number of lenses, a linear laser beam can beshaped so as to have a sinusoidal interference fringe profile (see FIGS.7C and 7G), which means that the invention is utilized most effectively.

However, even if the invention is utilized, energy unevenness due tolight interference still remains in a linear laser beam. Such unevennessmay be emphasized depending on the laser beam illumination conditions.

The degree of unevenness that occurs in this manner can be reduced byfinely adjusting the laser beam scanning direction. That is, laserprocessing may be performed while a linear laser beam is moved in adirection that exists in the plane of the linear laser beam and isdeviated by an angle y from the direction that exists in the plane ofthe linear laser beam and is perpendicular to the longitudinal directionof the linear laser beam. The angle y can be found in a range of 0<|tany|≦0.1. (|tan y|≢0)

If a polycrystalline semiconductor film is formed by laser-annealing asemiconductor film by using the optical system according to theinvention and a device such as a TFT liquid crystal display device ismanufactured by using the thus-formed polycrystalline semiconductorfilm, variations in the characteristics of the respective TFTs arereduced and there can be obtained a device capable of producinghigh-quality images.

If the invention is applied to laser annealing for manufacture of asemiconductor integrated circuit, the characteristics of elements formedon the same base member can be uniformized and there can be obtained acircuit exhibiting high performance.

Specific embodiments of the invention will be hereinafter described.

Embodiment 1

First, a method of forming a film to be subjected to laser illuminationwill be described as part of a manufacturing process of this embodiment.Three kinds of films to be subjected to laser illumination will bedescribed in this specification. The invention can effectively beapplied to any of those films.

First, for any of the three kinds of films, a 200-nm-thick silicon oxidefilm as an undercoat film and a 50-nm-thick amorphous silicon film areformed in this order on a 127-mm-square Corning 1737 glass substrate byplasma CVD. This film will be called a starting film in the followingdescription.

(Procedure of Forming Film A)

The starting film is subjected to hot bathing of 450° C. and 1 hour.This step is to reduce the hydrogen concentration of the amorphoussilicon film. This step is necessary because the film cannot withstandlaser energy if it contains an unduly large amount of hydrogen.

It is appropriate that the hydrogen concentration of the film be of theorder of 10²⁰ atoms/cm³. This film is called a silicon film A.

(Procedure of Forming Film B)

A nickel acetate layer is formed by applying a nickel acetate aqueoussolution of 10 ppm to the starting film by spin coating. It ispreferable that a surfactant be added to the nickel acetate aqueoussolution. Being extremely thin, the nickel acetate layer does notnecessarily assume a film form. However, this will not cause any problemin the ensuing steps.

The substrate on which the respective films have been laid in the abovemanner is subjected to thermal annealing of 600° C. and 4 hours. As aresult, the amorphous silicon film is crystallized into a crystallinesilicon film B.

In the above step, nickel as a catalyst element serves as nuclei forcrystal growth and the crystallization is thereby accelerated. It is byvirtue of the action of nickel that the crystallization can be performedat a low temperature of 600° C. in a short time of 4 hours. The detailsof this technique are disclosed in Japanese Unexamined PatentPublication No. 6-244104.

It is preferable that the concentration of the catalyst element be1×10¹⁵ to 1×10¹⁹ atoms/cm³. If the concentration is higher than 1×10¹⁹atoms/cm³, the crystalline silicon film exhibits metal properties andloses semiconductor properties. In this embodiment, the concentration ofthe catalyst element in the crystalline silicon film is 1×10¹⁷ to 5×10¹⁸atoms/cm³ in terms of the minimum value in the film. These values wereobtained through an analysis and a measurement by secondary ion massspectroscopy (SIMS).

(Procedure of Forming Film C)

A 700-λ-thick silicon oxide film is formed on the starting film byplasma CVD.

Then, a complete opening is formed in a portion of the silicon oxidefilm by photolithographic patterning.

Then, to form a thin oxide film in the opening, UV light is applied for5 minutes in an oxygen atmosphere. The thin oxide film is formed toimprove the wettability of the opening with respect to a nickel acetateaqueous solution to be introduced later.

Then, a nickel acetate aqueous solution of 100 ppm is applied to thefilm by spin coating, whereby nickel acetate is introduced into theopening. It is preferable that a surfactant be added to the nickelacetate aqueous solution.

Then, thermal annealing is performed at 600° C. for 8 hours and acrystal grows laterally from the nickel-introduced portion. In thisstep, nickel plays the same role as in Forming Film B. With theconditions of the embodiment, a lateral growth length of about 40 μm wasobtained.

In this manner, the amorphous silicon film is crystallized into acrystalline silicon film C which is a non-single-crystal silicon film.Subsequently, the silicon oxide film on the crystalline silicon film ispeeled and removed by using buffered hydrofluoric acid.

In the above manners, the non-single-crystal silicon films A-C areobtained.

Then, to improve the crystallinity, laser annealing is performed byusing an excimer laser.

FIG. 9 schematically shows a laser illumination system according to theembodiment.

In the laser illumination system of FIG. 9, a pulse laser beam isemitted from a laser oscillation device 201 and its traveling directionis adjusted by a pair of reflection mirrors 901. Then, the sectionalshape of the pulse laser beam is converted into a linear shape by anoptical system 902 according to the invention. Then, the pulse laserbeam is reflected by a mirror 207, focused by a cylindrical lens 208,and applied to a substrate 904 to be processed. A beam expander that canlimit the divergence angle of a laser beam and adjust the beam size maybe inserted between the pair of reflection mirrors 901.

The optical system 902, the mirror 207, and the cylindrical lens 208 arebasically the same as those shown in FIG. 5.

In this embodiment, the above-described optical system according to thethird aspect of the invention is employed as the optical system 902. Inthis embodiment, since the number of lenses of the cylindrical lensgroup 202 is seven (corresponds to (2n+1)), the cylindrical lens 501 isconstituted of two (corresponds to (n−1)) lenses in the optical systemof FIG. 5.

Now, a description will be made of a method of determining a distance bywhich the top and bottom lenses of the cylindrical lens 501 should bedeviated from each other.

In this embodiment, the pitch of a light interference fringe in a linearlaser beam that was formed by an arbitrarily selected one of theconstituent lenses of the cylindrical lens 501 and the lenses of theoptical system of FIG. 5 other than the cylindrical lens 501 was 0.1 mm,which corresponds to parameter d of the invention.

As described above, a deviation distance that is calculated according tod/(n−1) can distribute interference peaks to a largest extent in alinear laser beam.

Substituting d=0.1 mm and n=3 into the above formula, we obtain adistance of 0.05 mm. It goes without saying that according to theprinciple of superposition of waves the same effect is obtained even ifthe distance is changed to 0.15 mm, 0.25 mm, 0.35 mm, . . . at intervalsof 0.1 mm. As the distance is set longer, the effectively usable lengthin the longitudinal direction of a linear beam becomes shorter.

That is, where the top and bottom lenses of the cylindrical lens 501 aredeviated from each other, both end portions of a linear laser beam inthe longitudinal direction are blurred over the length that is equal tothe deviation distance. However, both end portions in the widthdirection are not blurred at all. Since both end portions of a linearlaser beam in the longitudinal direction can be located outside a devicearea, slight blurring causes no influence on the processing. On theother hand, since both end portions in the width direction are notblurred at all, no adverse influence is caused even if they are appliedto the device area.

In this embodiment, since n=3, the number of divided laser beams in thevertical direction (width direction of a linear beam) is determined by amultiple of (3−1). Specifically, N is set at 4 and the division numberis set at 8. The number of divided laser beams in the horizontaldirection (longitudinal direction of a linear beam) is (2·3+1)=7

The reason why the optical systems of FIGS. 2 and 5 are used is they canconvert the beam shape into a linear shape while averaging the energyunevenness existing in a beam before entrance to the optical system bydividing the beam and then superimposing the divided beams.

All linear laser beams used in the invention are basically the same as abeam obtained by the optical system of FIG. 5. The roles of the lensesshown in FIG. 5 will be described below.

The cylindrical lens groups 202 and 203 have roles of dividing a beam inthe horizontal and vertical directions. The cylindrical lenses 204 and501 have roles of combining the divided laser beams.

In this embodiment, an original beam is divided into eight beams in thevertical direction (width direction of a linear laser beam) and intoseven beams in the horizontal direction (longitudinal direction of alinear laser beam). Therefore, a linear laser beam is obtained bycombining 56 divided beams into a single beam. The beam energy profileis averaged in this manner.

Although the beam aspect ratio is variable from the viewpoint of theconfiguration of the optical system, easy-to-form beam shapes arerestricted by the sizes of the lenses and the combination of the focallengths. It is noted that the optical system being considered cannotchange the longitudinal length of a beam.

This embodiment is effective with either of the lens arrangement of FIG.8A or that of FIG. 8B. However, it is more effective with thearrangement of FIG. 8B.

Although the cylindrical lens group 202 and the cylindrical lens group203 are convex lens groups, they may be concave lens groups orconcave/convex-mixed lens groups. A laser beam may be divided by amethod other than the method using cylindrical lenses.

For example, FIG. 11A shows a concave/convex-mixed lens group havingapproximately the same function as the cylindrical lens group 202 shownin FIG. 5 and hence is replaceable with the latter. Or the cylindricallens group 203 and the cylindrical lens 204 shown in FIG. 5 may bereplaced by multi-phase lenses having approximately the same functions(see FIG. 11B). By disposing a multi-phase lens 1401 as shown in FIG.14, approximately the same beam as obtained by the optical system ofFIG. 6 can be formed. Further, the cylindrical lens 208 may be replacedby a multi-phase lens or a lens constituted of a plurality ofcylindrical lenses.

Where a lens whose constituent lenses are not congruous with each otheras typified by a concave/convex-mixed lens is used, it is preferablethat the constituent lenses be configured so as to produce parallelbeams having the same divergence angle. Otherwise, when divided beamsare recombined together, they are superimposed one on another in a statethat the individual beams have different sizes and shapes, as a resultof which the beam outline becomes unclear.

A XeCl excimer laser (wavelength: 308 nm) is used as the laseroscillation device 201. A KrF excimer laser (wavelength: 248 nm) and thelike may also be used.

A substrate 904 to be processed is mounted on a stage 905. The stage 905is moved straightly by a moving mechanism 903 in the direction that isperpendicular to the longitudinal direction of a linear laser beam andis included in the plane of the linear laser beam, to make it possibleto apply the linear laser beam to the top surface of the substrate 904while scanning it with the linear laser beam (see FIG. 9).

An apparatus shown in FIG. 10 will be described below. A cassette 1003accommodating a number of, for instance, 20, substrates 904 to beprocessed is placed in a load/unload chamber 1005. One substrate 904 ismoved from the cassette 1003 to an alignment chamber 1002 by a robot arm1004.

The alignment chamber 1002 is equipped with an alignment mechanism forcorrecting the positional relationship between the substrate 904 and therobot arm 1004. The alignment chamber 1002 is connected to theload/unload chamber 1005.

The substrate 904 is carried to a substrate transport chamber 1001 bythe robot arm 1004, and then moved to a laser illumination chamber 1006by the robot arm 1004.

Referring to FIG. 9, the width and the length of a linear laser beamthat is applied to the substrate 904 to be processed are set at 0.4 mmand 135 mm, respectively. The linear laser beam is formed by the lensarrangement of FIG. 5 in which the cylindrical lens group 203 isconstituted of eight lenses.

The energy density of a laser beam on the illumination surface is set ina range of 100-500 mJ/cm², for instance, 300 mJ/cm². The illuminationsurface is scanned with a linear laser beam while the stage 905 is movedin one direction at 1.2 mm/s. The oscillation frequency of the laseroscillation device 201 is set at 30 Hz. As a result, one point on theillumination surface is illuminated with 10 shots of laser beams. Thenumber of shots is selected in a range of 5 to 50.

After completion of the laser illumination, the substrate 904 isreturned to the substrate transport chamber 1001 by the robot arm 1004.Then, the substrate 904 is moved to the load/unload chamber 1005 andcaused to be accommodated in the cassette 1003 by the robot arm 1004.

The laser annealing step is thus finished. By repeating the above step,a number of substrates 904 can be processed consecutively one by one.

Although a linear laser beam is used in this embodiment, the inventionis effective even if any beam shape is employed that ranges from alinear shape to a square shape.

Either an n-channel TFT or a p-channel TFT can be manufactured by using,as an active layer, a semiconductor film formed by the above laserannealing. It is also possible to manufacture a structure that is acombination of an n-channel TFT and a p-channel TFT. Further, anelectronic circuit can be constructed by integrating a number of TFTs.

The above also applies to semiconductor films formed by laser annealingthat uses an optical system of any of the other embodiments. Where a TFTliquid crystal display device is manufactured by using a semiconductorfilm formed by laser annealing that uses the optical system of theinvention, it can produce high-quality images by virtue of smallvariations in the characteristics of the respective TFTs.

Embodiment 2

If a striped pattern cannot be eliminated properly in the firstembodiment, it means that the arrangement of the optical system or themanner of superposition of laser beams is inappropriate. In this case, ascanning direction that makes an interference fringe less conspicuousmay be selected by finely adjusting the substrate scanning directionwith a scanning direction changing device 906 (see FIG. 9).

That is, an adjustment is so made that scanning with a linear laser beamis performed in a direction that forms a small angle with the widthdirection of the linear laser beam.

Embodiment 3

Where the optical system arrangement shown in FIG. 8B is employed in thefirst embodiment, the pitch of an interference fringe can easily bederived through a calculation. This embodiment is directed to acalculation method therefor. First, the following consideration is madewith an assumption that the constituent lenses of the cylindrical lens501 are not deviated from each other. Such a cylindrical lens 501 is nowcalled a cylindrical lens 1206.

FIGS. 8A and 8B may be regarded as sectional views including thecylindrical lens group 202 shown in FIG. 5 and the cylindrical lens 501.

Where the optical system of FIG. 8B is employed, beams to be combined bythe cylindrical lens 1206 can be said to be plane waves.

In this case, as shown in FIG. 12, laser beams that enter thecylindrical lens 1206 after passing through two respective lenses 1201adjacent to the central lens among the lenses constituting thecylindrical lens group 202 intersect the illumination surface 1204 at anangle α.

Since a wave surface 1205 of a laser beam assumes a straight line inFIG. 12, straight lines representing wave surfaces that are drawn atintervals of a wavelength intersect the illumination surface 1204 atpoints having intervals β (see FIG. 13).

The relationship between the angle a and the intervals β can beexpressed by a formula including the wavelength λ, that is, β=λ/sin α.

The two lenses 1201 form stationary waves having the interval β on theillumination surface 1204. Two lenses 1202 form stationary waves havingan interval β/2 on the illumination surface 1204. Further, Two lenses1203 form stationary waves having an interval β/3 on the illuminationsurface 1204. Those stationary waves are combined on the illuminationsurface 1204 into a stationary wave as shown in FIG. 4A. Therefore, theinterval β coincides with the interval d between interference peaksshown in FIGS. 4A-4B and 7A-7G. This is understood by a simplecalculation.

A simple calculation shows that even if the position of the cylindricallens 1206 is moved with respect to the cylindrical lens group 202 in adirection of arrow 1207 (i.e., the right-left direction), almost novariation occurs in the interval d. This indicates that moving theconstituent lenses of the cylindrical lens 501 in the right or leftdirection in returning the cylindrical lens 1206 to the cylindrical lens501 does not influence the essence of the invention at all.

A relationship tan α=L/f holds where f is the local length of thecylindrical lens 1206 and L is the width of each constituent lens of thecylindrical lens group 202.

Since the angle α is sufficiently small, a relationship tan α˜sin α.Therefore, a formula β≧λf/L is obtained.

Since the relationship β=d generally holds as described above, d isapproximately given by λf/L.

Thus, the length of one period d of interference peaks appearing in abeam that is output from one constituent lens of the cylindrical lens501 shown in FIG. 5 can be determined without the need for conducting anactual measurement if the focal length f of the cylindrical lens 1206,the width L of each constituent lens of the cylindrical lens group 202,and the wavelength λ of the laser beam.

Where the optical system arrangement of FIG. 8A is employed, beams thatare output from the cylindrical lens 501 are spherical lens and hencethe above-obtained formula does not hold completely.

In this case, the value of d needs to be calculated through a numericalcalculation using a computer.

However, if the sum of the focal length f of the cylindrical lens 501and the focal length of the cylindrical lens group 202 is close to theinterval between the cylindrical lens 501 and the cylindrical lens group202, a value of d obtained by the above formula can be used.

Embodiment 4

This embodiment is directed to a case of manufacturing a TFT by using apolysilicon film formed by the above method.

A polysilicon film formed by the above method is patterned into anactive layer pattern on a TFT. A channel forming region andhigh-resistivity regions will be formed in the active layer pattern.After the formation of the active layer, a 100-nm-thick silicon oxidefilm as a gate insulating film is formed by plasma CVD.

Thereafter, a 400-nm-thick titanium film is formed by sputtering andthen patterned into a gate electrode. A 200-nm-thick anodic oxide filmis formed on the exposed surface of the titanium film pattern.

The anodic oxide film has a function of protecting the surface of thegate electrode electrically and physically as well as a function offorming high-resistivity regions called offset regions adjacent to thechannel forming region in a later step.

Then, phosphorus doping is performed by using the gate electrode and theanodic oxide film around it as a mask. Phosphorus serves as a dopant forsource and drain regions.

Source and drain regions are formed in a self-aligned manner by thephosphorus doping. Phosphorus is introduced at a dose of 5×10¹⁴ ions/cm²by using an ion doping apparatus. Phosphorus is activated byilluminating the active layer with laser light by the method of thefirst embodiment. The laser beam energy density is set at 200 mJ/cm².The appropriate energy density in this step depends on the kind oflaser, the illumination method, and the state of a semiconductor film.Therefore, the energy density should be adjusted to those factors. Thelaser illumination decreased the sheet resistance of the source anddrain regions to 1 kΩ/□.

Then, a 150-nm-thick silicon nitride film as an interlayer insulatingfilm is formed by plasma CVD and an acrylic resin film is formedthereon. The acrylic resin film is formed so as to have a minimumthickness of 700 nm. The resin film is used to planarize the surface.

Examples of usable materials other than acrylic-are polyimide,polyamide, polyimideamide, and epoxy. The resin film may be amultilayered film.

Then, after contact holes are formed, a source electrode and a drainelectrode are formed. An n-channel TFT is thus completed. Although inthis embodiment the n-channel TFT is manufactured because phosphorus isintroduced into the source and drain regions, to manufacture a p-channelTFT the source and drain regions may be doped with boron instead ofphosphorus.

When a liquid crystal display device, for instance, was manufactured byusing TFTs that were formed according to the invention, traces of thelaser processing were less conspicuous than in conventional cases.

As described above, the invention can greatly improve the intraplaneuniformity of the effect of laser annealing that uses a laser beam thathas been uniformized by dividing an original beam and recombining thedivided beams.

What is claimed is:
 1. A laser illumination method comprising the stepsof: causing a laser beam to pass through an optical system comprising:an optical lens for dividing the laser beam into N(n′−1) beams in avertical direction; a cylindrical lens group for dividing the laser beaminto (2n+1) beams in a horizontal direction; (n′−1) cylindrical lensesfor recombining the beams that are divided in the horizontal directionwhile superimposing the divided beams so that they are deviated fromeach other by d/(n′−1) in the horizontal direction; and a cylindricallens for recombining the beams that are divided in the verticaldirection; and crystallizing a semiconductor film by irradiating anillumination surface of a semiconductor film with the laser beam that isoutput from the optical system, wherein d is defined as an interval ofpeaks of an interference fringe that is formed on the illuminationsurface by a beam that has passed through one of the (n′−1) cylindricallenses and wherein N is a natural number, n is an integer that isgreater than or equal to 3, and n′ is an integer that satisfies 3<n′<n.2. A laser illumination method comprising the steps of: causing a laserbeam to pass through an optical system comprising: an optical lens fordividing the laser beam into N(n−1) beams in a vertical direction; acylindrical lens group for dividing the laser beam into (2n+1) beams ina horizontal direction; (n−1) cylindrical lenses for recombining thebeams that are divided in the horizontal direction while superimposingthe divided beams so that they are deviated from each other by d/(n−1)in the horizontal direction; and a cylindrical lens for recombining thebeams that are divided in the vertical direction; and crystallizing thesemiconductor film by irradiating an illumination surface of asemiconductor film with the laser beam that is output from the opticalsystem, wherein d is defined as an interval of peaks of an interferencefringe that is formed on the illumination surface by a beam that haspassed through one of the (n−1) cylindrical lenses and wherein N is anatural number, n is an integer that is greater than or equal to 3, andn′ is an integer that satisfies 3<n′<n.
 3. A laser illumination methodcomprising the steps of: causing a laser beam to pass through an opticalsystem comprising: an optical lens for dividing the laser beam intoN(n′−1) beams in a vertical direction; a cylindrical lens group fordividing the laser beam into (2n) beams in a horizontal direction;(n′−1) cylindrical lenses for recombining the beams that are divided inthe horizontal direction while superimposing the divided beams so thatthey are deviated from each other by d/(n′−1) in the horizontaldirection; and a cylindrical lens for recombining the beams that aredivided in the vertical direction; and crystallizing a semiconductorfilm by irradiating an illumination surface of a semiconductor film withthe laser beam that is output from the optical system, wherein d isdefined as an interval of peaks of an interference fringe that is formedon the illumination surface by a beam that has passed through one of the(n′−1) cylindrical lenses and wherein N is a natural number, n is aninteger that is greater than or equal to 3, and n′ is an integer thatsatisfies 3<n′<n.
 4. A laser illumination method comprising the stepsof: causing a laser beam to pass through an optical system comprising:an optical lens for dividing the laser beam into N(n=1) beams in avertical direction; a cylindrical lens group for dividing the laser beaminto (2n) beams in a horizontal direction; (n−1) cylindrical lenses forrecombining the beams that are divided in the horizontal direction whilesuperimposing the divided beams so that they are deviated from eachother by d/(n=1) in the horizontal direction; and a cylindrical lens forrecombining the beams that are divided in the vertical direction; andcrystallizing a semiconductor film by irradiating an illuminationsurface of a semiconductor film with the laser beam that is output fromthe optical system, wherein d is defined as an interval of peaks of aninterference fringe that is formed on the illumination surface by a beamthat has passed through one of the (n−1) cylindrical lenses and whereinN is a natural number, n is an integer that is greater than or equal to3, and n′ is an integer that satisfies 3<n′<n.
 5. The laser illuminationmethod according to claim 1, wherein on the illumination surface thelaser beam is a linear beam having a longer axis in the horizontaldirection.
 6. The laser illumination method according to claim 2,wherein on the illumination surface the laser beam is a linear beamhaving a longer axis in the horizontal direction.
 7. The laserillumination method according to claim 3, wherein on the illuminationsurface the laser beam is a linear beam having a longer axis in thehorizontal direction.
 8. The laser illumination method according toclaim 4, wherein on the illumination surface the laser beam is a linearbeam having a longer axis in the horizontal direction.
 9. The laserillumination method according to claim 1, wherein d is approximatelyexpressed by d=λf/L, where λ is a wavelength of the laser beam, f is afocal length of the (n′−1) cylindrical lenses, and L is a width of eachconstituent lens of the cylindrical lens group.
 10. The laserillumination method according to claim 2, wherein d is approximatelyexpressed by d=λf/L, where λ is a wavelength of the laser beam, f is afocal length of the (n′−1) cylindrical lenses, and L is a width of eachconstituent lens of the cylindrical lens group.
 11. The laserillumination method according to claim 3, wherein d is approximatelyexpressed by d=λf/L, where λ is a wavelength of the laser beam, f is afocal length of the (n′−1) cylindrical lenses, and L is a width of eachconstituent lens of the cylindrical lens group.
 12. The laserillumination method according to claim 4, wherein d is approximatelyexpressed by d=λf/L, where λ is a wavelength of the laser beam, f is afocal length of the (n−1) cylindrical lenses, and L is a width of eachconstituent lens of the cylindrical lens group.